SplineBasis-class {orthogonalsplinebasis}

Classes SplineBasis and OrthogonalSplineBasis

Description

Contains the matrix representation for spline basis functions. The OrthogonalSplineBasis class has the basis functions orthogonalized.

Objects from the Class

Objects can be created by calls of the form SplineBasis(knots, order) or to generate orthogonal spline basis functions directly OrthogonalSplineBasis(knots, order) or the short version OBasis(knots,order).

Slots

transformation:

Object of class "matrix" Only applicable on OrthogonalSplineBasis class, shows the transformation matrix use to get from regular basis functions to orthogonal basis functions.

knots:

Object of class "numeric"

order:

Object of class "integer"

Matrices:

Object of class "array"

Methods

deriv

signature(expr = "SplineBasis"): Computes the derivative of the basis functions. Returns an object of class SplineBasis.

dim

signature(x = "SplineBasis"): gives the dim as the order and number of basis functions. Returns numeric of length 2.

evaluate

signature(object = "SplineBasis", x = "numeric"): Evaluates the basis functions and the points provided in x. Returns a matrix with length(x) rows and dim(object)[2] columns.

integrate

signature(object = "SplineBasis"): computes the integral of the basis functions defined by \int\limits_{k_0}^x b(t)dt where k_0 is the first knot. Returns an object of class SplineBasis.

orthogonalize

signature(object = "SplineBasis"): Takes in a SplineBasis object, computes the orthogonalization transformation and returns an object of class OrthogonalSplineBasis.

plot

signature(x = "SplineBasis", y = "missing"): Takes an object of class SplineBasis and plots the basis functions for the domain defined by the knots in object.

plot

signature(x = "SplineBasis", y = "vector"): Interprets y as a vector of coefficients and plots the resulting curve.

plot

signature(x = "SplineBasis", y = "matrix"): Interprets y as a matrix of coefficients and plots the resulting curves.

References

General matrix representations for B-splines Kaihuai Qin, The Visual Computer 2000 16:177–186

See Also

SplineBasis

Examples

showClass("SplineBasis")

knots<-c(0,0,0,0:5,5,5,5)
(base <-SplineBasis(knots))
(obase<-OBasis(knots))
plot(base)
plot(obase)